Given a unit cube, what is the largest square that can be placed completely inside the cube?

I haven't come up with anything bigger than a unit square yet, despite several attempts.  It feels like there ought to be something bigger, but I guess my 3-D intuition is failing me.

I can come up with lots of bigger rectangles!

Edited on December 26, 2004, 4:38 pm

Posted by Steve Herman on 2004-12-26 16:38:15